Solutions and Solution Concentration: Mass, Volume, and Mass/Volume Percent

Solutions

Introduction to Solutions

Solutions are homogeneous mixtures composed of two or more substances. The substance present in the largest amount is called the solvent, while the other substances are called solutes. Understanding how to express the concentration of solutions is essential in chemistry, especially in laboratory and clinical settings.

Solution Concentration

Units of Concentration

The concentration of a solution describes the amount of solute dissolved in a specific amount of solution. Common units of concentration include:

• Mass percent (m/m)

• Volume percent (v/v)

• Mass/volume percent (m/v)

These units are used to quantify how much solute is present relative to the total solution, which is crucial for preparing solutions with precise properties.

Mass Percent (m/m)

Definition and Calculation

Mass percent (m/m) expresses the mass of solute in 100 grams of solution. It is calculated using the formula:

$\text{mass percent (m/m)} = \frac{\text{g of solute}}{\text{g of solute} + \text{g of solvent}} \times 100\%$

Alternatively, it can be used as a conversion factor:

$\text{mass percent (m/m)} = \frac{\text{g of solute}}{100\ \text{g of solution}}$

Example Calculation

When 8.00 g of KCl is dissolved in water to make 50.00 g of solution, the mass percent is:

$\text{mass percent} = \frac{8.00\ \text{g}}{50.00\ \text{g}} \times 100\% = 16.0\%\ (m/m)$

Stepwise Calculation Example

For a solution prepared by mixing 15.0 g of Na2CO3 and 235 g of H2O:

1. Calculate total mass of solution: 15.0 g + 235 g = 250.0 g

2. Calculate mass percent:

$\text{mass percent} = \frac{15.0\ \text{g}}{250.0\ \text{g}} \times 100\% = 6.00\%\ (m/m)$

Clinical Application

Medications are often described using mass percent. For example, a 0.1% (m/m) ointment contains 0.1 g of active ingredient per 100 g of ointment. This allows precise dosing in pharmaceutical preparations.

Using Mass Percent as a Conversion Factor

To find the amount of solute in a given mass of solution, use the mass percent as a conversion factor. For example, in 375 g of a 2.0% (m/m) NaCl solution:

$375\ \text{g solution} \times \frac{2.0\ \text{g NaCl}}{100\ \text{g solution}} = 7.5\ \text{g NaCl}$

Volume Percent (v/v)

Definition and Calculation

Volume percent (v/v) expresses the volume of solute in 100 mL of solution. It is calculated as:

$\text{volume percent (v/v)} = \frac{\text{mL of solute}}{\text{mL of solution}} \times 100\%$

Or as a conversion factor:

$\text{volume percent (v/v)} = \frac{\text{mL of solute}}{100\ \text{mL of solution}}$

Example Calculation

To prepare a 5.75% (v/v) ethanol solution from 2.25 mL of ethanol:

$2.25\ \text{mL ethanol} \times \frac{100\ \text{mL solution}}{5.75\ \text{mL ethanol}} = 39.1\ \text{mL solution}$

Application Example

To find the amount of bleach in a 320-mL bottle labeled as a 7.5% bleach solution:

$320\ \text{mL solution} \times \frac{7.5\ \text{mL bleach}}{100\ \text{mL solution}} = 24\ \text{mL bleach}$

Mass/Volume Percent (m/v)

Definition and Calculation

Mass/volume percent (m/v) expresses the mass of solute in 100 mL of solution. It is calculated as:

$\text{mass/volume percent (m/v)} = \frac{\text{g of solute}}{\text{mL of solution}} \times 100\%$

Or as a conversion factor:

$\text{mass/volume percent (m/v)} = \frac{\text{g of solute}}{100\ \text{mL of solution}}$

Example Calculation

If a patient receives 125 mL of a 20% (m/v) mannitol solution, the mass of mannitol administered is:

$125\ \text{mL solution} \times \frac{20\ \text{g mannitol}}{100\ \text{mL solution}} = 25\ \text{g mannitol}$

Determining Solution Volume for a Given Solute Mass

To provide 135 g of glucose using a 5% (m/v) glucose solution:

$135\ \text{g glucose} \times \frac{100\ \text{mL solution}}{5\ \text{g glucose}} \times \frac{1\ \text{L}}{1000\ \text{mL}} = 2.70\ \text{L solution}$

Conversion Factors from Percent Concentrations

Examples of Conversion Factors

Solution	Conversion Factor 1	Conversion Factor 2
8.50% (m/m) NaOH	8.50 g NaOH / 100 g solution	100 g solution / 8.50 g NaOH
5.75% (v/v) ethanol	5.75 mL ethanol / 100 mL solution	100 mL solution / 5.75 mL ethanol
4.8% (m/v) HCl	4.8 g HCl / 100 mL solution	100 mL solution / 4.8 g HCl

Summary Table: Percent Concentration Formulas

Type	Formula	Interpretation
Mass percent (m/m)	$\frac{\text{g solute}}{\text{g solute} + \text{g solvent}} \times 100\%$	g solute per 100 g solution
Volume percent (v/v)	$\frac{\text{mL solute}}{\text{mL solution}} \times 100\%$	mL solute per 100 mL solution
Mass/volume percent (m/v)	$\frac{\text{g solute}}{\text{mL solution}} \times 100\%$	g solute per 100 mL solution

Additional info: These concentration units are foundational for preparing laboratory solutions, calculating dosages in medicine, and analyzing chemical mixtures in both academic and professional settings.